Problem: Simplify the following expression: $ q = \dfrac{-9}{8} + \dfrac{-r - 5}{r - 6} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{r - 6}{r - 6}$ $ \dfrac{-9}{8} \times \dfrac{r - 6}{r - 6} = \dfrac{-9r + 54}{8r - 48} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{-r - 5}{r - 6} \times \dfrac{8}{8} = \dfrac{-8r - 40}{8r - 48} $ Therefore $ q = \dfrac{-9r + 54}{8r - 48} + \dfrac{-8r - 40}{8r - 48} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-9r + 54 - 8r - 40}{8r - 48} $ $q = \dfrac{-17r + 14}{8r - 48}$